**Important Concepts and Formulas on Algebraic Expressions**

1. A symbol that can take different
values is called a variable.

2. A symbol having a fixed numerical
value is called a constant.

3. We can form an algebraic expression
involving variables and constants using basic operations (+, –, ×, ÷) to
connect them. For example, 5xy – 8 is an algebraic expression involving the
variables x, y and constants 5 and 8.

4. The signs ‘+’ and ‘–’ separate the
expression into various parts. These parts are called terms.

5. When terms have the same variables
and if the powers of the variables are same, then they are called like terms,
else they are unlike terms.

6. The numerical factor in a term is
called its coefficient.

7. An algebraic expression having
exponents as non-negative integers is called a polynomial.

8. Polynomials having one, two and three
terms are called monomials, binomials and trinomials, respectively.

9. The degree of a polynomial is the
degree of term having the highest exponent (or sum of exponents). For example,
the degree of 3x + 2x

^{2}y – 7 is 3 (therefore, the term 2x^{2}y has degree as 2 + 1 = 3).
10. To add or subtract algebraic
expressions, we add or subtract the like terms together but keep the unlike
terms as such. For example, (5x + 2xy + 7z + y) + (–3y + x – 3xy) = (5x + x) +
(2xy – 3xy) + (–3y + y) + (7z) = 6x + (–xy) + (–2y) + 7z or 6x –xy – 2y + 7z.

11. To find the product of two
expressions, multiply each term of the first expression with each term of second
expression.

12. If an equation is true for all values
of the variable, it is called an identity.

13. Some of the identities are:

·
(a
+ b)

^{2}= a^{2}+ 2ab + b^{2}
·
(a
– b)

^{2}= a^{2}– 2ab + b^{2}
·
(a
+ b) (a – b) = a

^{2}– b^{2}